For A∈ L (X), B∈ L (Y) and C∈ L (Y, X) we denote by MC the operator defined on X⊕ Y by
[AC0B]. In this article, we study defect set DΣ=(Σ (A)∪ Σ (B))∖ Σ (MC) for different spectra …

For A∈ B (X), B∈ B (Y) and C∈ B (Y, X), let MC be the operator defined on X⊕ Y by
[AC0B]. In this paper, we study defect set (Σ (A)∪ Σ (B))∖ Σ (MC), where Σ is the Browder …

Without question, the dichotomy spectrum is a central tool in the stability, qualitative and
geometric theory of nonautonomous dynamical systems. When dealing with such linear …

J. Math. Anal. Appl. On the perturbations of spectra of upper triangular operator matrices Page 1
J. Math. Anal. Appl. 347 (2008) 315–322 Contents lists available at ScienceDirect J. Math. Anal …

Let and be complex separable infinite‐dimensional Hilbert spaces. Given the operators and,
we define where is an unknown element. In this paper, a necessary and sufficient condition …

A bounded linear operator A acting on a Banach space X is said to be an upper triangular
block operators of order n, and we write A ∈ UT _ n (X), if there exists a decomposition of X …

Abstract Let M_C=\left () be a 2× 2 upper triangular operator matrix acting on the Banach
space X× Y. We prove that σ _ τ (A) ∪ σ _ τ (B)= σ _ τ (M_C) ∪ W, where W is the union of …

RIESZ POINTS OF UPPER TRIANGULAR OPERATOR MATRICES Introduction Let T ∈ B (X),
the algebra of all bounded linear operators on Page 1 PROCEEDINGS OF THE AMERICAN …

The closed range and Fredholm properties of the upper-triangular operator matrix $ M=(A,
C; 0, B)\in\mathcal {B}({\mathcal H} _1\oplus {\mathcal H} _2) $ are studied, where …

This paper is concerned with the self-adjoint perturbations of the spectra for the upper
triangular partial operator matrix with given diagonal entries. A necessary and sufficient …